Adaptive Multicarrier CDMA Space-Time Receivers - Adaptive Signal Processing in Wireless Communications - page 279

C K n + 1

∑∑ , ∑

u u u

Y = b ψ u + N n . (10. 22)

n k n ′ kn , nkn ′ ,,

u = 1 kK =− nn ′= − 1

Without loss of generality, let us focus on the detection of the n th symbol carried by
the k t h carrier of the desired user assigned index d ∈{1, … C }, i.e., b k d ,n d . Using equation
(10.22) and defining a vector V as a matrix V reshaped column-wise, we can rewrite the
observation matrix for a desired user d with respect to its n th symbol of carrier k targeted
for detection in the following simpler vector form:

C K n + 1

∑ ∑ ∑

d d u u

Ys = U + s U

n k n , nkn , , kn ′′ , nkn ′′ ′ ,,



desiredsignal

u
ud

1


=
≠

kK ′=− nn ′= − 1

 

d

I MAIkn

,,

K n + 1 +

∑ +

n 1

∑ ∑ s U

d d d d

+ + s U N , (10.23)

kn ′′ ′′ , nkn , , kn , ′ ′ nkn , , n

k K

kk

′ =−

′≠

nn ′= − 1 nn

nn

′′=−
′≠

1

     

d d

I I

ICI, kn , ISI, kn ,

d d d

= sU ++ I N ,

kn , n kn , kn , n

where s k ′, n ′ = ψ k ′, n b k ′, n ′ and (ψ k,n ) 2 are the n ′ th signal component of the k ′ th carrier of user
u , and the received power of user u over carrier k , respectively. The total interference
I d k,n includes three types of interference: (1) the multiple access interference I d MAI, k,n is
the interference due to the N c carriers from the other in-cell users u ≠ d ; (2) the inter-
carrier interference I d ICI, k,n is the interference due to the other carriers, k ′ ≠ k , from
the same user d ; and (3) the intersymbol interference I d ISI, k,n is the interference due to
the same carrier k from the same user d . The noise vector N n , which comprises the pre-
processed thermal noise and the interference due to out-of-cell users, is assumed to be
uncorrelated both in space and time with variance σ 2 .
In previous work [32], we proposed a receiver named MC-STAR. MC-STAR assumes
the interference I d k,n as another contribution to the noise N n . Hence, the signal compo-
nent of the desired user's carrier is extracted by spatiotemporal maximum ratio combin-
ing (MRC) as follows:

H

d

ˆ

UY

H

d

ˆ

d nkn ,, n

s = W Y = , (10. 24)

kn , MRCkn ,, n

2

d

ˆ

U

nkn ,,

where anywhere in the chapter the notation ˆ stands for an estimate of a given variable
α, (.) H is the Hermitian operator, and W d MRC , k,n is the MRC beamformer. Equation (10.23)